In this brief article, chaosbased cryptography is discussed from a point of view which I believe is closer to the spirit of both cryptography and chaos theory than the way the subject has been treated recently by many researchers. I hope that, although this paper raises more questions than provides answers, it nevertheless contains seeds for future work.… (More)

We discuss the relationship between cryptography and chaos theory, and similarities of their crucial concepts such as mixing property and sensitivity to changes in initial conditions and parameters. A systematic procedure for design of encryption algorithms based on chaotic maps is suggested. We present an example based on logistic map.  2001 Elsevier… (More)

This paper and its companion (Part I) are devoted to to the analysis of the application of a chaotic piecewise-linear one-dimensional (PL1D) map as Random Number Generator (RNG). In Part I, we have mathematically analyzed the information generation process of a class of PL1D maps. In this paper, we find optimum parameters that give an RNG with lowest… (More)

Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy rates—measures of new disorder per new observed value—are equal for ergodic finite-alphabet information sources (discrete-time… (More)

Digital chaotic ciphers have been investigated for more than a decade. However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed. We propose a chaotic Feistel cipher and a chaotic uniform cipher. Our plan is to examine crypto… (More)

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We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent… (More)

Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which makes possible implementing a trapdoor mechanism. In this paper we study a public key cryptosystem based on such… (More)